Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 1, January 2005, Pages 565 - 598

Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs

Authors
S.N.M. Ruijsenaars
Corresponding Author
S.N.M. Ruijsenaars
Available Online 1 January 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.45How to use a DOI?
Abstract
In a previous paper (Regular and Chaotic Dynamics 7 (2002), 351­391, Ref. [1]), we obtained various results concerning reflectionless Hilbert space transforms arising from a general Cauchy system. Here we extend these results, proving in particular an isometry property conjectured in Ref. [1]. Crucial input for the proof comes from previous work on a special class of relativistic Calogero-Moser systems. Specifically, we exploit results on action-angle maps for the pertinent systems and their relation to the 2D Toda soliton tau-functions. The reflectionless transforms may be viewed as eigenfunction transforms for an algebra of higher-order analytic difference operators.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - Supplement 1
Pages
565 - 598
Publication Date
2005/01
ISBN
91-974824-3-9
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.45How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - S.N.M. Ruijsenaars
PY  - 2005
DA  - 2005/01
TI  - Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs
JO  - Journal of Nonlinear Mathematical Physics
SP  - 565
EP  - 598
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.45
DO  - https://doi.org/10.2991/jnmp.2005.12.s1.45
ID  - Ruijsenaars2005
ER  -